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The decimal number 0.15625 10 represented in binary is 0.00101 2 (that is, 1/8 + 1/32). (Subscripts indicate the number base .) Analogous to scientific notation , where numbers are written to have a single non-zero digit to the left of the decimal point, we rewrite this number so it has a single 1 bit to the left of the "binary point".
For example, the smallest positive number that can be represented in binary64 is 2 −1074; contributions to the −1074 figure include the emin value −1022 and all but one of the 53 significand bits (2 −1022 − (53 − 1) = 2 −1074). Decimal digits is the precision of the format expressed in terms of an equivalent number of decimal digits.
This property also makes it straightforward to represent a timestamp as a fractional day, so that 2025-01-11.54321 can be interpreted as five decimal hours, 43 decimal minutes and 21 decimal seconds after the start of that day, or a fraction of 0.54321 (54.321%) through that day (which is shortly after traditional 13:00).
Time Technology's Samui Moon binary-coded sexagesimal wristwatch. This clock reads 3:25. Binary clocks that display time in binary-coded sexagesimal also exist. Instead of representing each digit of traditional sexagesimal time with one binary number, each component of traditional sexagesimal time is represented with one binary number, that is, using up to 6 bits instead of only 4.
Swift introduced half-precision floating point numbers in Swift 5.3 with the Float16 type. [20] OpenCL also supports half-precision floating point numbers with the half datatype on IEEE 754-2008 half-precision storage format. [21] As of 2024, Rust is currently working on adding a new f16 type for IEEE half-precision 16-bit floats. [22]
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1.67 minutes (or 1 minute 40 seconds) 10 3: kilosecond: 1 000: 16.7 minutes (or 16 minutes and 40 seconds) 10 6: megasecond: 1 000 000: 11.6 days (or 11 days, 13 hours, 46 minutes and 40 seconds) 10 9: gigasecond: 1 000 000 000: 31.7 years (or 31 years, 252 days, 1 hour, 46 minutes, 40 seconds, assuming that there are 7 leap years in the interval)
But the decimal number 10 is encoded in hexadecimal as 0A 16 and in BCD as 10 16. Thus a BCD 10 16 interpreted as a hexadecimal encoding erroneously represents the decimal number 16. For example, the SMS protocol uses BCD encoding for dates, so some mobile phone software incorrectly reported dates of messages as 2016 instead of 2010.